"We have the votes we need," Gillibrand said today at a press conference on Capitol Hill. "We've had indications from several Republicans that they very much want to vote for this bill.

"They would like to vote for a stand-alone bill," she said. "There is general agreement on a new pay-for that we're going to offer, so the hope is to get to the bill as soon as the START bill is completed."

The bill was put to a test vote on Dec. 9, but supporters found themselves three votes short of the 60 needed to proceed to debate and a final vote. The measure failed 57-42.

Republican Mark Kirk of Illinois has now voiced his support for the bill. With his vote and that of Majority Leader Sen. Harry Reid, who switched his vote to "no" at the last moment, a parliamentary move that allows him to bring the measure up again for a vote, Democrats need just one more Republican vote to pass the bill.

And now that Republicans are no longer bound to their pledge to avoid voting on anything except issues of taxes and funding, some GOP senators are considering voting in favor of the 9/11 measure.

With Democrats one vote short, all eyes are now falling on three Republican Senators who have hinted that they could support the bill -- Susan Collins and Olympia Snowe of Maine and Lisa Murkowski of Alaska.

Collins is the GOP's point person on the matter, and has been working with Gillibrand to find new means to off-set the costs of the $7.4 billion bill.

"I support the 9/11 health bill on the merits, and I have talked with Senator Gillibrand about the need for legitimate ways of offsetting its cost," Collins said in a statement on Thursday. "If the Majority Leader were to bring the bill to the floor with appropriate offsets, I would support the legislation."

The off-set in the House-passed measure would close tax loopholes for foreign companies, a move that Collins has objected to on the grounds that it would violate international tax treaties.

Today Gillibrand said that the new off-set would be a 2 percent fee on procurement contracts for certain countries, combined with a visa fee.

"I urge my Republican colleagues to end the filibuster, engage in an open and respectful debate, and let each senator decide for themselves whether the heroes and victims of September 11th deserve quality health treatment and appropriate compensation for their tremendous loss and sacrifice," Gillibrand said earlier this week.